As the sun sets on a Saturday evening, downtown Manhattanites are just getting started on their plans for the evening — and so are their toddlers.

Inside a hip TriBeCa playspace, a throng of pajama-clad youngsters is tearing around; one dives into a brightly colored ball pit, while another few race downstairs to jump on the trampoline. Some kids, clearly regulars, know each other already. One tearful new arrival is taken in by some friendly peers. Baby sitters attempt to keep up with their young charges.

This is Project Playdate, where hip parents deposit their young ones while they head off for a few hours of kid-free fun on the weekend. Scrambling for a baby sitter is so passé — for basically the same amount you’d pay for a sitter ($45 for the first child, $25 for each additional sibling, for three hours), parents can hire the Project Playdate ladies for Saturday night kiddie pizza parties from 5:30 to 8:30.

During the evening’s “free play” period, before the pizza arrives, they all scamper around the two-level hangout.

But even among the fun and games, some youngsters are already training to be the leaders of tomorrow. Project Playdate founder Amanda Raposo, 23, mandates a gold-star system that rewards children who go above and beyond to be helpful.

“Because of our leadership program, kids are actively looking for opportunities to include others, to share with others,” she says. “It’s a very friendly environment.”

For the kids, though, is it not a little weird being thrust into a makeshift pajama party with other random children?

Not if you ask Zachary Prager, 5. “It’s fun,” says Zachary. “I come to every pajama party. My favorite part is to eat like 10 pieces of pizza and drink two drinks.”

As befits a younger clientele, the evening is stuffed full of activities, which ramp up after the initial half-hour of free play.

“Who’s hungry for pizza?” cries Raposo at the stroke of 6, and everyone races to the dining area for fresh organic slices (cut into small sizes for tiny hands) and juice. The evening’s live entertainment starts at 6:30, when in-house DJ and singer Jay Stolar busts out some tunes for the young dancers — Lady Gaga and LMFAO, and a screensaver projected on the wall for a disco effect — after which he brings out his acoustic guitar for a singalong.

Not everyone is feeling the dance vibe, though.

“I’m not in the mood,” says a bespectacled girl named Emma Gelman, sounding 6-going-on-36, who instead opts to help the sitters clean up the other room in exchange for a gold star.

The night concludes with a bit of arts and crafts and the whole group chilling out in front of a movie — tonight’s is the animated hit “Cloudy With a Chance of Meatballs.”

The cheerfully progressive company currently runs on Saturday evenings at an independent play space called Playgarden in TriBeCa, and the first Friday evening of every month at Kidville in Union Square.

The pajama-party company launched three years ago, but has recently exploded in popularity — the group’s first Brooklyn night kicks off July 20 in Park Slope, followed by the Upper West Side in September.

“We’ve gotten incredibly positive feedback from parents, who consistently ask us to expand to different locations,” Raposo says.

The company is the brainchild of Raposo, who, while at NYU studying social work and social entrepreneurship, came up with the idea to combine child care with charity for low-income mothers. All the proceeds, after Project Playdate’s expenses, go to support Powerhouse NYC, a local housing facility for young homeless mothers and their children.

The baby sitters, all volunteers, are highly vetted by Raposo and her team: Many are NYU students focusing their studies on early childhood development and social services, while others are brought in through the service College Nannies and Tutors.

Parents can register on the company’s Web site, projectplaydate.org. A maximum of 30 kids from ages 1 to 7 is allowed (28 on one recent night, including a couple of last-minute additions), and the ratio of sitters is one for every three kids.

“The sitters are consistently great,” says Inga Reznik, Emma’s mom. Though she says the convenient location was one of the biggest selling points, Reznik is a fan of the link to Powerhouse.

“It’s the whole package,” she says. “The sitters and the money going to a good cause.”

Plus, Reznik can rest assured knowing her kid will be enjoying a robust social schedule for Saturday evening, just like she is.

“We’ve got our pajama parties down to a science,” says Raposo, who announces on the dot of 6:30 that it is officially song and dance time. “Short attention spans, you know!”